Don't know if there are any SBR semi-auto Thompsons but there was a pistol variation. It was simply a Thompson built without a buttstock (pistolgrip only) from the factory and thusly they were registered as handguns.
I think the the time might be affected if the barrel was cut down too much. There is a lot of bolt to move in a Thompson and I would imagine that it needs all the power it can get to reciprocate.